Given the xp nerf to party members and the fact that F2P is 1k gold cap I see no reason to sell power levels.
If you do want to sell power levels:
The only way to sell them is by when both the Power leveler and carried party members are added into the dungeon through separate queues OR your toon is F2P.
That being said the only 100% no shenanigans way to power level people is with a 20 f2p. It will be weaker than lower levels but you won't have to deal with queue shuffling. You might even get a low level twink in your dungeons if you're quing tbc or legion. F2P Power level is still faster than questing for the vast majority of players. The normal 20 bis is super weak but a pre-patch bis 20 is very good. If you are not one of those lucky few than you'll have to settle for the normal bis.
I as a seasoned player would never buy a power level from a F2P. So I figure your customers would either be new, uneducated, friends, and or super lazy.
The best carrier is Bear: it has hots,dots,hp,armor,power,speed. Tab+moonfire+thrash+autorun=win
run into an issue? well regrowth WILL top anyone off. ANYONE!!!!!!
anything else and your asking for cooldown issues and speed problems or que time issues.
2nd best: doesn't matter bear is best.
honorable mentions:
Frost DK at 14 with fenyr trinket and tincture can just walk past everything spamming howling blast. (weak armor)
12 WW monk can pretty much 1 shot any mob pack every 20ish sec with fist of fury
Arcane Mage anywhere from 10-14. pretty much will end up as tank due to raw dmg. (weak armor but get shield at 11)
Prot paladin any level but requires way to much haste to be effective compared to other classes.
best races for speeding through dungeons:
Worgen for extra speed ability
Light Forged Goat people for their insane lights judgment ability.
Horde what? lol